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A mathematical model for separation of suspensions with a non-Newtonian disperse medium by dual-stage pressurized flotation in a cylindrical-conical hydrocyclone is developed. A system of differential equations of the convective diffusion and movement of a complex of particles-bubbles is solved by a numerical method. The concentration field is modeled, and integral separation indicators are determined. Values of structural parameters of the hydrocyclone for which the separation indicators depend heavily on the taper angle of the conical section of the housing and the rheological properties of the disperse medium are established.It is demonstrated that dual-stage pressurized flotation makes it possible to reduce considerably the residual concentration of solid-phase particles as compared with single-stage flotation.Cylindrical-conical hydrocyclones, which provide for high efficiency of the separation of dissimilar chemical systems in various branches of industry, are distinguished by high reliability, and simplicity of installation, and do not require extensive energy outlays for the separation process. Dual-stage pressurized flotation, which is realized in a cylindrical-conical hydrocyclone, can be used in a number of productions to achieve a high degree of extraction of solid-phase (SP) particles from a suspension.Dual-stage flotation takes place in the following manner: a preliminarily aerated suspension is delivered tangentially under elevated pressure (up to 0.8 MPa) to the cylindrical chamber of a hydrocyclone via an inlet pipe mounted in its upper section. By forming a rotating film (the velocity components are: circumferential v ϕ , axial v z , and radial v r ), the suspension that has entered the hydrocyclone moves downward along its walls. When the pressure is reduced to atmospheric, supersaturation of dissolved gas is created, and the suspension "effervesces." The centrifugal force moves the SP particles toward the wall of the housing of the hydrocyclone, while Archimedes buoyant centripetal force moves the air bubbles toward the SP particles to the surface of the film.In the first stage of pressurized flotation, formation of flotation complexes, which carry SP particles onto the surface of the film in a foam layer, the latter being removed by the upper branch pipe of the hydrocyclone, occurs when the SP particles collide with the gas bubbles. Bubbles of secondary gas that enters via the porous wall of the housing have a diam-

Numerical simulation is used to study the dynamics of non-Newtonian free-surface flow in a cylindrical-conical hydrocyclone. For different angles of taper of the conical section of the hydrocyclone, the pressure and velocity distributions are calculated, together with the dependence of the fluid film thickness on the axial coordinate. The effect of the rheological properties of the fluid and the controlling similarity parameters on the flow dynamics is studied.

Recommendations for optimization of structural parameters of a cylindrical hydrocyclone used to degas heterogeneous liquid media possessing non-Newtonian properties are set forth on the basis of results of numerical modeling. The mathematical degassing model takes into account the effect of inertial and Coriolis forces, and the associated liquid mass during the movement of a gas bubble. A system of differential equations in partial derivatives, which describes the degassing of heterogeneous media in a hydrocyclone, is reduced to ordinary differential equations, and is solved by the numerical method. The influence exerted on the degassing process by structural parameters of a cylindrical hydrocyclone and rheologic properties of the liquid is analyzed.Yablonskii [1] solves the problem of the film flow of a non-Newtonian liquid in a cylindrical direct-flow hydrocyclone by a numerical method using complete equations of rheodynamics. The problem of the degassing of heterogeneous liquid systems possessing non-Newtonian properties was solved in [2-6]; however, a description of the degassing process in a hydrocyclone during the film flow of a non-Newtonian liquid with a freely forming surface on the basis of solution of a complete system of rheodynamics equations with consideration of the associated liquid mass and the action of inertial and Coriolis forces has not been given until now, and is of significant theoretical and applied interest.The purpose of the present study is to select structural parameters of a cylindrical hydrocyclone for the degassing of heterogenous liquid media on the basis of results of numerical analysis.A cylindrical hydrocyclone in which the liquid film has minimal thickness is best suited for the degassing of heterogeneous liquid media; this ensures high degassing effectiveness, whereas a significant increase in the thickness of the liquid film occurs in the conical section of the housing in a cylindrical-conical hydrocyclone.The hydrocyclone consists of a cylindrical housing in which a non-Newtonian liquid containing gas bubbles is introduced tangentially via an inlet pipe mounted in its upper section. On rotating, the liquid that has entered the housing of the hydrocyclone flows downward along its walls, possessing radial v r , circumferential v ϕ , and axial v z velocity components. Gas bubbles are driven from the liquid by Archimedes centripetal force into a foam layer on the surface of the film.